WASHINGTON (CNN) -- Congressional Republicans offered what they call a "centrist, practical" plan to overhaul the U.S. health care system Tuesday, one they say would be the cheapest of any option proposed so far.

House Republicans say their health care plan is a better package than the Senate version.

Illinois Rep. Mark Kirk said the package put together by moderate Republicans in the House of Representatives would be far cheaper than a plan being drawn up in the Senate. A preliminary review of that plan by the Congressional Budget Office found it would cost about $1 trillion over 10 years to extend health insurance to 16 million people who otherwise would not be covered -- about a third of the roughly 45 million now uninsured.

"I think this plan that we put forward is more centrist, more bipartisan and would be at significantly lower cost," Kirk said. He said no cost estimate had been prepared for the measures he put forth Tuesday, but asserted its elements would require less money from taxpayers than other proposals.

The package announced by the GOP "Tuesday Group" includes some perennial Republican favorites such as regulatory relief, an individual tax break for purchasing health insurance and limits on malpractice lawsuits. It also would encourage insurers to pool their coverage to a greater extent than currently allowed, which Kirk and other supporters say has worked well in California.

But it also emphasizes preventive care, computerizing patient records and reducing "defensive medicine" by promoting treatments proven effective -- all principles the White House has endorsed, as well.

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The centerpiece of the plan, Kirk said, is a "Medical Rights Act" that would keep government out of "decisions made by you and your doctor." He said the plans were drawn up during four months of talks with dozens of groups, including patient advocates, doctors, nurses, employers and "other interested groups."

The proposal came as the conservative GOP leadership in the House stepped up attacks on the proposal being drafted by Senate Democrats. House Minority Leader John Boehner, R-Ohio, said Monday's budget office report showed "millions of Americans" would lose their current insurance.

"President Obama says the problem with our health care is that we spend too much, and if you look at all the proposals, clearly they are going to spend trillions of dollars of additional money that we don't have -- that we're going to have to borrow -- in order to finance their scheme," Boehner told reporters.

The report projected that the number of people covered by employer-based health care plans would fall by about 15 million by 2017. In the same year, about 39 million people would be covered by policies purchased through a health insurance "exchange" of the type Obama has proposed.

White House spokesman Robert Gibbs told reporters Tuesday that a bill is still being drafted and "has many twists and turns to go."

"One incomplete older proposal I don't think is indicative of where we are now," he said.